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In-plane deformation of cantilever plates with applications to lateral force microscopy
Rev. Sci. Instrum. 75, 878 (2004); doi:10.1063/1.1667252
Published 10 March 2004
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The in-plane deformation of atomic force microscope (AFM) cantilevers under lateral loading is commonly assumed to have negligible effect in comparison to other deformation modes and ignored. In this article, we present a theoretical study of the behavior of cantilevers under lateral loading, and in so doing establish that in-plane deformation can strongly contribute to the total deformation, particularly for rectangular cantilevers of high aspect ratio (length/width). This has direct implications to lateral force microscopy, where the neglect of in-plane deformation can contribute to significant quantitative errors in force measurements and affect the interpretation of measurements. Consequently, criteria and approaches for minimizing the effects of in-plane deformation are presented, which will be of value to users and designers of AFM cantilevers. Accurate analytical formulas for the in-plane spring constants of both rectangular and V-shaped cantilevers are also presented. ©2004 American Institute of Physics.
| History: | Received 15 August 2003; accepted 12 January 2004; published 10 March 2004 |
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http://link.aip.org/link/?RSINAK/75/878/1 |
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REFERENCES (19)
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- This only occurs for V-shaped cantilevers with small arm width ratio d/b. For example, the V-shaped cantilever (Microlevers) by Veeco, 112 Robin Hill Road, Santa Barbara, CA 93117, with dimensions L = 323 µm, b = 215 µm, d = 21 µm, h/t = 5.5, has an equivalent rectangular cantilever of aspect ratio L/c = 8 with
y~1. The lateral stiffness of the equivalent rectangular cantilever is 0.6 times lower than the V-shaped cantilever. - We note that any imaging tip deformation (Ref. 17) will reduce the difference between the lateral spring constants of the V-shaped and rectangular cantilever/tip combinations, provided the same tip is attached to both cantilevers.
